Bnach 空间中远达和同时远达问题的适定性

本文研究Bn ach空间X中远达和同时远达问题的适定性,在集合的Husdorff距离下,对X中的闭凸子集D和相对弱紧的有界闭子集K,证明了下述结果:若D关于K严格凸和有Kdec性质,则D中所有使远达问题mxx,K是适定的点x全体在D中是Gδ型集.作为应用,得到了同时远达问题适定性的类似结果.     

Banach空间中关于有界集的同时远达问题的适定性

本文研究Banach空间中关于有界集的同时远达问题的适定性,在集合的Hausdorff距离下,证明了：对自反局部一致凸Banach空间中的闭有界集K,使所有关于K的同时远达问题是适定的紧凸子集A全体在紧凸子集全体中是Gδ型集．     

非自反实Banach空间中的广义共同远达点问题的适定性

设C是实Banach空间X中有界闭凸子集且O是C的内点,G是X中非空有界闭的相对弱紧子集.记K(X)为X的非空紧凸子集并赋Hausdorff距离.称广义共同远达点问题maxc(A,G)是适定的是指它有唯一解(x0,z0)且它的每个极大化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下,我们运用不同于DeBlasi,MyjalandPapini和Li等人的方法证明了集{A∈K(X);maxc(A,G)是适定的}含有K(X)中稠Gδ集,这本质地推广和延拓了包括DeBlasi,MyjakandPapini和Li等人在内的近期相应结果.     

赋范线性空间中同时远达点的唯一性

1 引言 设X为一实赋范线性空间,给定X中的子集G和有界子集K,令(?)和C分别表示X的所有非空有界子集与相对紧子集的全体,对A∈B,记 若x_(0)∈K满足sup||a-x_(0)||=Fk(A),则称x_(0)是A关于K的同时远达点,A关于K的同时远达点的全体记为Q_(K)(A),即     

远达函数的可导性与远达点的存在性

该文考察Banach空间上的远达函数的可导性与远达点的存在性间的关系，指出某些Banach空间上的远达函数(对有界闭集而言)具等于1或-1的单侧方向导数蕴含远达点的存在性，并给出了Banach空间CLUR和LUR的新等价刻划．     

多目标优化中的简化定理及其应用

１ 引言 设Ｘ是实的Ｂａｎａｃｈ空间,Ｓ 　 Ｘ是闭子集． 考虑下述多目标优化问题：其中ｆｋ,ｋ∈Ｎ≡｛１,…,ｎ｝,ｇｉ,ｉ∈Ｍ≡｛１,…,ｍ｝,ｈｉ,ｊ∈Ｐ≡｛１,…,ｐ｝均是定义在某开集（包含Ｓ）上的局部Ｌｉｐｓｃｈｉｔｚ函数． 集合Ｓ０＝｛ｘ∈Ｓ：ｇｉ（ｘ）≤０,ｉ∈Ｍ,,ｈｉ（ｘ）＝０,ｊ∈Ｐ｝称为（ＶＰ）的可行解集．（ＶＰ）的局部有效解和局部弱有效解的定义见［２］．设φ：Ｘ→Ｒ是局部Ｌｉｐｓｃｈｉｔｚ函数,则　φ（ｘ）称为φ在ｘ处的Ｃｌａｒｋｅ广义梯度［３］． 关于非光滑多目标优化问题（Ｖ…     

一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为

设Ｘ是有Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｔ：Ｃ→Ｃ是一个渐近非扩张映象．证明了，如果｛ｘ_ｎ：ｎ≥１｝是Ｔ的几乎轨道，则序列｛ｘ０｝弱几乎收敛到集合∩from∞to(ｎ＝１)ｃｏ｛ｘ_i：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．     

Devil＇s Staircase of K－H Waves in a SeparatingShearLayerwithAcousticExcitation

Ｄｅｖｉｌ＇ｓＳｔａｉｒｃａｓｅｏｆＫ－ＨＷａｖｅｓｉｎａＳｅｐａｒａｔｉｎｇＳｈｅａｒＬａｙｅｒｗｉｔｈＡｃｏｕｓｔｉｃＥｘｃｉｔａｔｉｏｎＹ．Ｆ．ＤＯＮＧ，Ｚ．Ｌ．ＷＥＩａｎｄＣ．ＸＵｆ（Ｄｅｐｔ．ｏｆＭｅｃｈａｎｉｃｓａｎｄＥｎｇｉｎｅｅｒｉｎ...     

Banach空间上凸函数的Gateaux可微点

Ｂａｎａｃｈ空间上凸函数的Ｇａｔｅａｕｘ可微点杨富春云南大学本文总设定Ｘ是实Ｂａｎａｃｈ空间，Ｄ是ｘ的非空开凸子集，ｊ：Ｄ→Ｒ是连续的凸函数。ｆ在ｘ∈Ｄ的Ｇａｔｅａｕｘ导数，简称Ｇ导数。记在ｘ点６可微若则记为ｆ在ｘ∈Ｇ（ｆ；Ｄ）的Ｇ导数｝。已经知道，...     

A New Class of Banach Spaces with Uniform Normal Structure

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＸｂｅａｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅ ,ａｎｄｌｅｔＳ(Ｘ) ={ｘ∈Ｘ :ｘ =1 }ｂｅｔｈｅｕｎｉｔｓｐｈｅｒｅｏｆＸ .Ｉｎ 1 94 8,ＢｒｏｄｓｋｉｉａｎｄＭｉｌｍａｎ[1]ｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｇｅｏｍｅｔｒｉｃｃｏｎｃｅｐｔ:　Ｄｅｆｉｎｉｔｉｏｎ 1　ＡＢｏｕｎｄｅｄ ,ｃｏｎｖｅｘｓｕｂｓｅｔＫｏｆａＢａｎａｃｈｓｐａｃｅＸｉｓｓａｉｄｔｏｈａｖｅｎｏｒｍａｌｓｔｒｕｃｔｕｒｅｉｆｅｖｅｒｙｃｏｎｖｅｘｓｕｂｓｅｔＨｏｆＫｔｈａｔｃｏｎｔａ…     

Farthest points in weakly compact sets

LetS be a weakly compact subset of a Banach spaceB. We show that of all points inB which have farthest points inS contains a denseG ₅ ofB. Also, we give a necessary and sufficient condition for bounded closed convex sets to be the closed convex hull of their farthest points in reflexive Banach spaces.     

关于随机最远点

首先给出在随机赋范模中子集的随机最远点的概念．进一步,利用随机一致凸性和经典一致凸性之间的联系证明了下面的结果：令（E,｜｜·｜｜）为完备的随机一致凸的随机赋范模,S为E中几乎处处有界并在（ε, λ）一拓扑下的闭子集,则具有S中随机最远点的集合稠于E．     

Chebyshev Centers that are Not Farthest Points

In this paper, we address the question whether in a given Banach space, a Chebyshev center of a nonempty bounded subset can be a farthest point of the set. We obtain a characterization of two-dimensional real strictly convex spaces as those ones where a Chebyshev center cannot contribute to the set of farthest points of a subset. In dimension greater than two, every non-Hilbert smooth space contains a subset whose Chebyshev center is a farthest point. We explore the scenario in uniformly convex Banach spaces and further study the roles played by centerability and Mcompactness in the scheme of things to obtain a step by step characterization of strictly convex Banach spaces.     

Farthest points of sets in uniformly convex banach spaces

LetS be a closed and bounded set in a uniformly convex Banach spaceX. It is shown that the set of all points inX which have a farthest point inS is dense. Letb(S) denote the set of all farthest points ofS, then a sufficient condition for to hold is thatX have the following property (I): Every closed and bounded convex set is the intersection of a family of closed balls.     

Farthest points and strong convexity of sets

We consider the existence and uniqueness of the farthest point of a given set A in a Banach space E from a given point x in the space E. It is assumed that A is a convex, closed, and bounded set in a uniformly convex Banach space E with Fréchet differentiable norm. It is shown that, for any point x sufficiently far from the set A, the point of the set A which is farthest from x exists, is unique, and depends continuously on the point x if and only if the set A in the Minkowski sum with some other set yields a ball. Moreover, the farthest (from x) point of the set A also depends continuously on the set A in the sense of the Hausdorff metric. If the norm ball of the space E is a generating set, these conditions on the set A are equivalent to its strong convexity.     

广义共同逼近问题的适定性

设C是实Banach空间X中有界闭凸子集且0是C的内点，G是X中非空闭的有界相对弱紧子集.记K(X)为X的非空紧凸子集全体并赋Hausdorff距离，KG(X)为集合｛A∈K(X)；A∩G=｝的闭包.称广义共同逼近问题minC(A,G)是适定的是指它有唯一解(x0,z0)，且它的每个极小化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下，证明了｛A∈K(X)；minC(A，G)是适定的｝含有KG(X)中稠Gδ子集，这本质地推广和延拓了包括De Blasi,Myjak and Papini［1］、Li［2］和De Blasi and Myjak［3］等人在内的近期相应结果.     

Farthest points in reflexive locally uniformly rotund Banach spaces

IfS is a bounded and closed subset of a Banach spaceB, which is both reflexive and locally uniformly rotund, then, except on a set of first Baire category, the points inB have farthest points inS.     

关于有界闭凸集上的弱滴性质的注记

证明了“若K是Banach空间X中的有界闭凸集,0∈intK,则K有弱滴性质当且仅当K⁰有(WS)性质.”从而证明了文[1]中提出的一个问题.